{"paper":{"title":"Noncommutative harmonic analysis on semigroup and ultracontractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Xiao Xiong","submitted_at":"2016-03-14T13:04:09Z","abstract_excerpt":"We extend some classical results of Cowling and Meda to the noncommutative setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a noncommutative space $L_p(\\mathcal{M}),$ and let the functions $\\phi$ and $\\psi$ be regularly related. We prove that the semigroup $(T_t)_{t>0}$ is $\\phi$-ultracontractive, i.e. $\\|T_t x\\|_\\infty \\leq C \\phi(t)^{-1} \\|x\\|_1$ for all $x\\in L_1(\\mathcal{M})$ and $ t>0$ if and only if its infinitesimal generator $L$ has the Sobolev embedding properties: $\\|\\psi(L)^{-\\alpha} x\\|_q \\leq C'\\|x\\|_p$ for all $x\\in L_p(\\mathcal{M}),$ where $1<p<q<\\infty$ and $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04247","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}